Sean Murphy has composed a nicely detailed page on Molly Malone. He writes:

As well as being known and sung internationally, the popular song ‘Cockles and Mussels’ has become a sort of unofficial anthem of Dublin city. The song’s tragic heroine Molly Malone and her barrow have come to stand as one of the most familiar symbols of the capital. In addition, Molly’s international pulling power is shown by the fact that she scores hundreds of ‘hits’ on the Internet, many of them relating to ‘Irish pubs’ bearing her name. It seems perfectly natural therefore that Molly should have been commemorated by erecting a statue to her in Dublin, which monument has become a familiar landmark at the corner of Grafton Street and Suffolk Street. Let us now travel back in time to see what we can find out about the real Molly Malone.